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Short-term optimal scheduling of wind-photovoltaic-hydropower-thermal-pumped hydro storage coupled system based on a novel multi-objective priority stratification method
基于新型多目标优先级分层法的风-光-水电-热-抽水蓄能耦合系统短期最优调度

Kaiyan Wang a , ∗ a , ∗ ^(a,^(**)){ }^{\mathrm{a},{ }^{*}}, Hengtao Zhu a a ^(a){ }^{\mathrm{a}}, Jian Dang a a ^(a){ }^{\mathrm{a}}, Bo Ming b b ^(b){ }^{\mathrm{b}}, Xiong Wu c Wu c Wu^(c)\mathrm{Wu}^{\mathrm{c}}
王 a , ∗ a , ∗ ^(a,^(**)){ }^{\mathrm{a},{ }^{*}} 开燕 ， 朱亨涛 a a ^(a){ }^{\mathrm{a}} ， 党 a a ^(a){ }^{\mathrm{a}} 健 ， 博明 b b ^(b){ }^{\mathrm{b}} ， 熊 Wu c Wu c Wu^(c)\mathrm{Wu}^{\mathrm{c}} a a ^(a){ }^{a} School of Electrical Engineering, Xi'an University of Technology, Xi'an, 710048, China
a a ^(a){ }^{a} 习安理工大学 电气工程学院， 中国 习安市 710048 b b ^(b){ }^{\mathrm{b}} State Key Laboratory of eco-hydraulics in northwest arid region of China, Xi'an, 710048, Shaanxi Province, China
b b ^(b){ }^{\mathrm{b}} 西北干旱区生态水力学国家重点实验室， 习'an， 710048， 陕西省 c S School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049, China c S School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049, China  ^("c S School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049, China "){ }^{\text {c S School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049, China }}

A R T I C L E I N F O

Keywords:  关键字：

Renewable energy sources consumption
可再生能源消耗
Pumped hydro storage  抽水蓄能
Coupled system  耦合系统
Priority stratification  优先级分层
Enhanced plant growth simulation algorithm
增强的植物生长模拟算法

Abstract  抽象

In the new power system with high proportion of uncertain renewable energy sources (RES), there is a defect of RES consumption at the expense of other power sources’ operational efficiency. This paper proposes a short-term optimal scheduling model of wind-photovoltaic-hydropower-thermal-pumped hydro storage (WPHTPHS) coupled system, which realizes the multiple optimization objectives involving minimizing operation cost of thermal power units, maximizing clean energy power generation, minimizing net load fluctuation and thermal power regulation. First, to overcome the dimension disaster problem in the solution space of high-dimensional random variables, a method for pre-solving integer state variables is proposed. Then, a novel multi-objective solution strategy of priority stratification-coupled feedback combined with improved plant growth simulation algorithm is designed. Finally, the effectiveness and superiority of the proposed model and solution method are demonstrated by case studies, and the numerical results show that the number of startups and shutdowns, standard deviation of output and operating cost of thermal power units are reduced by 90.9 % , 65.34 % 90.9 % , 65.34 % 90.9%,65.34%90.9 \%, 65.34 \%, and 14.01 % 14.01 % 14.01%14.01 \% respectively, compared with traditional wind-photovoltaic-thermal strategy. This study contributes to resolving the relationship between conflicting objectives and highlighting the potential advantages of WPHTPHS coupled system to maximize overall performance from economic and stability perspectives.
在不确定可再生能源 （RES） 比例较高的新电力系统中，存在以牺牲其他电源的运行效率为代价的 RES 消耗缺陷。本文提出了一种风-光-水电-热抽蓄能（WPHTPHS）耦合系统短期最优调度模型，实现了最小化火电机组运行成本、最大化清洁能源发电、最小化净负荷波动和火电调节等多重优化目标。首先，为克服高维随机变量求解空间中的维数灾难问题，提出了一种预求解整数状态变量的方法。然后，设计了一种新颖的优先级分层耦合反馈多目标求解策略，并结合改进的植物生长模拟算法。最后，通过算例分析证明了所提模型和求解方法的有效性和优越性，数值结果表明，与传统的风-光-热策略相比，火电机组的启动和关闭次数、出力标准差和运行成本分别降低了 90.9 % , 65.34 % 90.9 % , 65.34 % 90.9%,65.34%90.9 \%, 65.34 \% 和 14.01 % 14.01 % 14.01%14.01 \% 。本研究有助于解决相互冲突的目标之间的关系，并强调 WPHTPHS 耦合系统的潜在优势，以从经济和稳定性的角度最大限度地提高整体性能。

Nomenclature  命名法
Abbreviations  缩写 P Gi i , t P Gi  i , t P_("Gi "i,t)P_{\text {Gi } i, t} Output of TPU i i ii at period t t tt
期间 t t tt TPU i i ii 的输出
P W,t P W,t  P_("W,t ")P_{\text {W,t }} Output of wind at period t t tt
期间 t t tt 的风输出
P P v , t P P v , t P_(Pv,t)P_{P v, t} Output of PV at period t t tt
周期 t t tt 的 PV 输出
CNY Chinese Yuan  人民币 P D , t P D , t P_(D,t)P_{\mathrm{D}, t} Load demand at period t t tt
期间 t t tt 的负荷需求
EPGSA Enhanced plant growth simulation algorithm
增强的植物生长模拟算法		 P PHD , t P PHD , t P_(PHD,t)P_{\mathrm{PHD}, t} Residual load after wind, PV and PHS integrated
风后剩余负载，PV 和 PHS 集成
EGM Extensive growth mode  粗放型生长模式 P D − WPV , t P D − WPV , t P_(D-WPV,t)P_{\mathrm{D}-\mathrm{WPV}, \mathrm{t}} Residual load after wind and PV integrated
风电和光伏一体化后的剩余负荷
FGM Fine growth mode  精细生长模式 P H j , t P H j , t P_(Hj,t)P_{H j, t} Output of hydropower unit j j jj at period t t tt
水电机组 j j jj 发电量 t t tt
GHP General hydropower plants
一般水电站		 P P H , R P P H , R P_(PH,R)P_{P H, R} Rated power of PHS  PHS 的额定功率
HSO Hierarchical sequence optimization
分层序列优化		 P P H k , t P P H k , t P_(PHk,t)P_{P H k, t} Pumping/generating power of PHS k k kk at period t t tt
期间 t t tt PHS k k kk 的抽水/发电功率
PV Photovoltaic  光伏 P G i , max / P G , min P G i , max / P G , min {:[P_(Gi,max)//],[P_(G,min)]:}\begin{aligned} & P_{\mathrm{G} i, \max } / \\ & P_{\mathrm{G}, \min } \end{aligned} Maximum/Minimum power of TPU i i ii
TPU i i ii 的最大/最小功率
Abbreviations P_("Gi "i,t) Output of TPU i at period t P_("W,t ") Output of wind at period t P_(Pv,t) Output of PV at period t CNY Chinese Yuan P_(D,t) Load demand at period t EPGSA Enhanced plant growth simulation algorithm P_(PHD,t) Residual load after wind, PV and PHS integrated EGM Extensive growth mode P_(D-WPV,t) Residual load after wind and PV integrated FGM Fine growth mode P_(Hj,t) Output of hydropower unit j at period t GHP General hydropower plants P_(PH,R) Rated power of PHS HSO Hierarchical sequence optimization P_(PHk,t) Pumping/generating power of PHS k at period t PV Photovoltaic "P_(Gi,max)// P_(G,min)" Maximum/Minimum power of TPU i| Abbreviations | | $P_{\text {Gi } i, t}$ | Output of TPU $i$ at period $t$ | | :---: | :---: | :---: | :---: | | | | $P_{\text {W,t }}$ | Output of wind at period $t$ | | | | $P_{P v, t}$ | Output of PV at period $t$ | | CNY | Chinese Yuan | $P_{\mathrm{D}, t}$ | Load demand at period $t$ | | EPGSA | Enhanced plant growth simulation algorithm | $P_{\mathrm{PHD}, t}$ | Residual load after wind, PV and PHS integrated | | EGM | Extensive growth mode | $P_{\mathrm{D}-\mathrm{WPV}, \mathrm{t}}$ | Residual load after wind and PV integrated | | FGM | Fine growth mode | $P_{H j, t}$ | Output of hydropower unit $j$ at period $t$ | | GHP | General hydropower plants | $P_{P H, R}$ | Rated power of PHS | | HSO | Hierarchical sequence optimization | $P_{P H k, t}$ | Pumping/generating power of PHS $k$ at period $t$ | | PV | Photovoltaic | $\begin{aligned} & P_{\mathrm{G} i, \max } / \\ & P_{\mathrm{G}, \min } \end{aligned}$ | Maximum/Minimum power of TPU $i$ |
(continued)  （续）
PHS Pumped hydro storage  抽水蓄能 P H , max / P H , min P H , max / P H , min {:[P_(H,max)//],[P_(H,min)]:}\begin{aligned} & P_{\mathrm{H}, \max } / \\ & P_{\mathrm{H}, \min } \end{aligned} Maximum/Minimum power of GHP j j jj
GHP j j jj 的最大/最小功率
RES Renewable energy sources  可再生能源 P PHgk, P PHgk,  P_("PHgk, ")P_{\text {PHgk, }} max/ P P H g , min P P H g ,  min  P_(PHg," min ")P_{P H g, \text { min }}
P PHgk, P PHgk,  P_("PHgk, ")P_{\text {PHgk, }} 麦克斯/ P P H g , min P P H g ,  min  P_(PHg," min ")P_{P H g, \text { min }} 		Maximum/Minimum generating power of PHS k k kk
PHS k k kk 的最大/最小发电功率
TPUs  热塑性聚氨酯 Thermal power units  火力发电机组 P P H p k , max ′ P P H p k , min P P H p k , max ′ P P H p k , min {:[P_(PHpk,)],[ max'],[P_(PHpk,min)]:}\begin{aligned} & P_{P H p k,} \\ & \max \prime \\ & P_{P H p k, \min } \end{aligned} Maximum/Minimum pumping power of PHS k k kk
PHS k k kk 的最大/最小泵送功率
WPHTPHS Wind-photovoltaic-hydropower-thermalpumped hydro storage
风光水电热抽水蓄能		 P 0 i P 0 i P_(0i)P_{0 i} Power corresponding to the minimum specific consumption
对应于最小比消耗的功率
Parameters and variables  参数和变量 Q j t Q j t Q_(jt)Q_{j t} Average water flow used by GHP j j jj at period t t tt
GHP j j jj 在此期间 t t tt 使用的平均水流量
a i , b i , c i a i , b i , c i a_(i),b_(i),c_(i)a_{i}, b_{i}, c_{i} Fuel cost coefficientsof TPU i i ii
TPU i i ii 的燃料成本系数		 r d i / r u i r d i / r u i r_(di)//r_(ui)r_{d i} / r_{u i} Downward/Upward ramp rate for TPU i i ii
TPU i i ii 的下降/上升速率
(continued on next page)  （下一页继续）
(continued) PHS Pumped hydro storage "P_(H,max)// P_(H,min)" Maximum/Minimum power of GHP j RES Renewable energy sources P_("PHgk, ") max/ P_(PHg," min ") Maximum/Minimum generating power of PHS k TPUs Thermal power units "P_(PHpk,) max' P_(PHpk,min)" Maximum/Minimum pumping power of PHS k WPHTPHS Wind-photovoltaic-hydropower-thermalpumped hydro storage P_(0i) Power corresponding to the minimum specific consumption Parameters and variables Q_(jt) Average water flow used by GHP j at period t a_(i),b_(i),c_(i) Fuel cost coefficientsof TPU i r_(di)//r_(ui) Downward/Upward ramp rate for TPU i (continued on next page)| (continued) | | | | | :---: | :---: | :---: | :---: | | PHS | Pumped hydro storage | $\begin{aligned} & P_{\mathrm{H}, \max } / \\ & P_{\mathrm{H}, \min } \end{aligned}$ | Maximum/Minimum power of GHP $j$ | | RES | Renewable energy sources | $P_{\text {PHgk, }}$ max/ $P_{P H g, \text { min }}$ | Maximum/Minimum generating power of PHS $k$ | | TPUs | Thermal power units | $\begin{aligned} & P_{P H p k,} \\ & \max \prime \\ & P_{P H p k, \min } \end{aligned}$ | Maximum/Minimum pumping power of PHS $k$ | | WPHTPHS | Wind-photovoltaic-hydropower-thermalpumped hydro storage | $P_{0 i}$ | Power corresponding to the minimum specific consumption | | Parameters and variables | | $Q_{j t}$ | Average water flow used by GHP $j$ at period $t$ | | $a_{i}, b_{i}, c_{i}$ | Fuel cost coefficientsof TPU $i$ | $r_{d i} / r_{u i}$ | Downward/Upward ramp rate for TPU $i$ | | | | | (continued on next page) |
https://doi.org/10.1016/j.energy.2024.133190
Received 7 June 2024; Received in revised form 8 September 2024; Accepted 14 September 2024
2024 年 6 月 7 日接收;2024 年 9 月 8 日以修订版接收;录用日期 2024 年 9 月 14 日
Available online 14 September 2024
2024 年 9 月 14 日在线提供
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(continued)  （续）
A hydropower conversion constant
水电转换常数		 r i 1 / r i 2 / r k i r i 1 / r i 2 / r k i [r_(i1)//r_(i2//)rk],[i]\begin{aligned} & \hline r_{i 1} / r_{i 2 /} r k \\ & i \end{aligned} Random numbers uniformly distributed in the interval [ 0 , 1 ] [ 0 , 1 ] [0,1][0,1]
在区间 [ 0 , 1 ] [ 0 , 1 ] [0,1][0,1] 内均匀分布的随机数
Cfuel  燃料 Coal-fired cost  燃煤成本 s i , t s i , t s_(i,t)s_{i, t} State of TPU i i ii at period t t tt
TPU i i ii t t tt 期间的状态 ( 1 / 0 ) ( 1 / 0 ) (1//0)(1 / 0)
Cco 2 Cco 2 Cco_(2)\mathrm{Cco}_{2} Carbon dioxide emission cost
二氧化碳排放成本		 T Time series in 24 h
24 小时的时间序列
C C CC Cost per unit of carbon emission (0.13CNY/ kg )
单位碳排放成本 （0.13CNY/ kg）

吨 i，t- 1 / 1 / 1//1 / 吨 我 我我I， T-1
Ton i,t-
1 / 1 / 1//1 / Toff i i ii,
t-1
Ton i,t- 1// Toff i, t-1| Ton i,t- | | :--- | | $1 /$ Toff $i$, | | t-1 |
 Successive hours that TPU i i ii has been on/off at period t t tt-1
TPU i i ii 在时段 t t tt -1 开启/关闭的连续小时数
C C CC Carbon emission coefficient per unit power of TPUs (0.741 kg/kW•h)
TPU 每单位功率的碳排放系数 （0.741 kg/kW•h）

锤头 i/ 唐 i
Tup i/
Tdown i
Tup i/ Tdown i| Tup i/ | | :--- | | Tdown i |
 Minimum up/down time of TPU i i ii
TPU i i ii 的最小启动/关闭时间
h j t h j t h_(jt)h_{j t} Water head of GHP j j jj at period t t tt
期间 t t tt GHP j j jj 水头		 u k , t u k , t u_(k,t)u_{k, t} State factor of PHS k k kk at period t t tt
期间 t t tt PHS k k kk 的状态因子
k d k d k_(d)k_{d} Load spinning reserve rate
负载旋转储备率		 u i u i u_(i)u_{i} Discrete quantity with equal probability 0 or 1
概率相等的离散量 0 或 1
k r k r k_(r)k_{r} Number of the optimal solution
最优解数		 V u , t / V d , t V u , t / V d , t V_(u,t)//V_(d,t)V_{u, t} / V_{d, t} Capacity of upper/lower reservoirs at period t t tt
期间 t t tt 上/下水库容量
N t N t N_(t)N_{t} Number of TPUs  TPU 数量 W min / W max W min / W max {:[W_(min)//],[W_(max)]:}\begin{aligned} & W_{\min } / \\ & W_{\max } \end{aligned} Minimum/Maximum available power generation capacity
最小/最大可用发电容量
N PH N PH  N_("PH ")N_{\text {PH }} Number of PHS  PHS 数量 z j k z j k z_(jk)\mathrm{z}_{\mathrm{j} k} Generated chaotic variable
生成的混沌变量
N h N h N_(h)N_{h} Number of hydropower units
水力发电机组数量		 η Hj η Hj eta_(Hj)\eta_{\mathrm{Hj}} Efficiency of GHP j j jj
GHP j j jj 的效率
N k e N k e N_(ke)N_{k e} Number of growth steps in EGM
EGM 中的增长步骤数		 η PH η PH  eta_("PH ")\eta_{\text {PH }} Efficiency of PHS  PHS 的效率
N rmax N rmax  N_("rmax ")N_{\text {rmax }} Maximum repetitions of optimal solution
最优解的最大重复次数		 η g / η p η g / η p eta_(g)//eta_(p)\eta_{g} / \eta_{p} Generating/Pumping power efficiency of PHS
PHS 的发电/抽水功率效率
PSR req,t  PSR 要求，t

期间 t t tt 的旋转储备要求
Spinning reserve requirements at period
t t tt
Spinning reserve requirements at period t| Spinning reserve requirements at period | | :--- | | $t$ |
 τ g / τ p τ g / τ p tau_(g)//tau_(p)\tau_{g} / \tau_{p} Number of periods of PHS generating/pumping power
PHS 产生/泵送功率的周期数
PSR W , t / P S R P v , t  PSR  W , t / P S R P v , t {:[" PSR "W","t//PSR],[quad Pv","t]:}\begin{aligned} & \text { PSR } W, t / P S R \\ & \quad P v, t \end{aligned} Spinning reserve requirements to cope with the uncertainty of wind/PV
应对风能/光伏不确定性的旋转储备要求		 ω 1 / ω 2 ω 1 / ω 2 omega1//omega2\omega 1 / \omega 2 Regulating factor, the value can be larger in the early iteration and then gradually reduced
调节因子，该值在早期迭代中可以较大，然后逐渐减小
Ppeak D, t / Pvalley D, t  Ppeak D,  t /  Pvalley D,  t {:[" Ppeak D, "t//],[" Pvalley D, "t]:}\begin{aligned} & \text { Ppeak D, } t / \\ & \text { Pvalley D, } t \end{aligned} Load demand at peak/ valley period
高峰/低谷时段的负载需求		 δ δ delta\delta Deviation threshold  偏差阈值

Ppeak W，t/ Ppeak P v , t P v , t Pv,tP v, t Pvalley W， t / P t / P t//Pt / P 谷 P v , t P v , t Pv,tP v, t 值
Ppeak W,t/
Ppeak P v , t P v , t Pv,tP v, t
Pvalley W,
t / P t / P t//Pt / P valley
P v , t P v , t Pv,tP v, t
Ppeak W,t/ Ppeak Pv,t Pvalley W, t//P valley Pv,t| Ppeak W,t/ | | :--- | | Ppeak $P v, t$ | | Pvalley W, | | $t / P$ valley | | $P v, t$ |
 Available wind/PV at peak/valley load period.
高峰/谷负荷期的可用风能/光伏。		 λ λ lambda\lambda Positive factor ( 0 < λ < 1 ( 0 < λ < 1 (0 < lambda < 1(0<\lambda<1 ), determined by overall deviation and operational ability of PHS
正因子 ( 0 < λ < 1 ( 0 < λ < 1 (0 < lambda < 1(0<\lambda<1 ），由 PHS 的整体偏差和操作能力决定
PSR,peak req, t / P S R , valley req, t  PSR,peak req,  t / P S R ,  valley req,  t {:[" PSR,peak req, "],[t//PSR","],[" valley req, "t]:}\begin{aligned} & \text { PSR,peak req, } \\ & t / P S R, \\ & \text { valley req, } t \end{aligned} Spinning reserve requirements at peak/ valley load
峰值/谷载时的纺纱储备要求		 Δ λ k i Δ λ k i Delta lambda ki\Delta \lambda k i Step of the i th i th  i_("th ")i_{\text {th }} component of the node k k kk
节点 i th i th  i_("th ")i_{\text {th }} k k kk 组件的步骤
P i t , j P i t , j P_(it,j)P_{i t, j} Output of unit i i ii at period t t tt of the j th j th  j_("th ")j_{\text {th }} seed
j th j th  j_("th ")j_{\text {th }} 种子周期 t t tt 的单位 i i ii 输出		 Δ t Δ t Delta t\Delta t Period interval  周期间隔
A hydropower conversion constant "r_(i1)//r_(i2//)rk i" Random numbers uniformly distributed in the interval [0,1] Cfuel Coal-fired cost s_(i,t) State of TPU i at period t (1//0) Cco_(2) Carbon dioxide emission cost T Time series in 24 h C Cost per unit of carbon emission (0.13CNY/ kg ) "Ton i,t- 1// Toff i, t-1" Successive hours that TPU i has been on/off at period t-1 C Carbon emission coefficient per unit power of TPUs (0.741 kg/kW•h) "Tup i/ Tdown i" Minimum up/down time of TPU i h_(jt) Water head of GHP j at period t u_(k,t) State factor of PHS k at period t k_(d) Load spinning reserve rate u_(i) Discrete quantity with equal probability 0 or 1 k_(r) Number of the optimal solution V_(u,t)//V_(d,t) Capacity of upper/lower reservoirs at period t N_(t) Number of TPUs "W_(min)// W_(max)" Minimum/Maximum available power generation capacity N_("PH ") Number of PHS z_(jk) Generated chaotic variable N_(h) Number of hydropower units eta_(Hj) Efficiency of GHP j N_(ke) Number of growth steps in EGM eta_("PH ") Efficiency of PHS N_("rmax ") Maximum repetitions of optimal solution eta_(g)//eta_(p) Generating/Pumping power efficiency of PHS PSR req,t "Spinning reserve requirements at period t" tau_(g)//tau_(p) Number of periods of PHS generating/pumping power " PSR W,t//PSR quad Pv,t" Spinning reserve requirements to cope with the uncertainty of wind/PV omega1//omega2 Regulating factor, the value can be larger in the early iteration and then gradually reduced " Ppeak D, t// Pvalley D, t" Load demand at peak/ valley period delta Deviation threshold "Ppeak W,t/ Ppeak Pv,t Pvalley W, t//P valley Pv,t" Available wind/PV at peak/valley load period. lambda Positive factor (0 < lambda < 1 ), determined by overall deviation and operational ability of PHS " PSR,peak req, t//PSR, valley req, t" Spinning reserve requirements at peak/ valley load Delta lambda ki Step of the i_("th ") component of the node k P_(it,j) Output of unit i at period t of the j_("th ") seed Delta t Period interval| A | hydropower conversion constant | $\begin{aligned} & \hline r_{i 1} / r_{i 2 /} r k \\ & i \end{aligned}$ | Random numbers uniformly distributed in the interval $[0,1]$ | | :---: | :---: | :---: | :---: | | Cfuel | Coal-fired cost | $s_{i, t}$ | State of TPU $i$ at period $t$ $(1 / 0)$ | | $\mathrm{Cco}_{2}$ | Carbon dioxide emission cost | T | Time series in 24 h | | $C$ | Cost per unit of carbon emission (0.13CNY/ kg ) | Ton i,t- <br> $1 /$ Toff $i$, <br> t-1 | Successive hours that TPU $i$ has been on/off at period $t$-1 | | $C$ | Carbon emission coefficient per unit power of TPUs (0.741 kg/kW•h) | Tup i/ <br> Tdown i | Minimum up/down time of TPU $i$ | | $h_{j t}$ | Water head of GHP $j$ at period $t$ | $u_{k, t}$ | State factor of PHS $k$ at period $t$ | | $k_{d}$ | Load spinning reserve rate | $u_{i}$ | Discrete quantity with equal probability 0 or 1 | | $k_{r}$ | Number of the optimal solution | $V_{u, t} / V_{d, t}$ | Capacity of upper/lower reservoirs at period $t$ | | $N_{t}$ | Number of TPUs | $\begin{aligned} & W_{\min } / \\ & W_{\max } \end{aligned}$ | Minimum/Maximum available power generation capacity | | $N_{\text {PH }}$ | Number of PHS | $\mathrm{z}_{\mathrm{j} k}$ | Generated chaotic variable | | $N_{h}$ | Number of hydropower units | $\eta_{\mathrm{Hj}}$ | Efficiency of GHP $j$ | | $N_{k e}$ | Number of growth steps in EGM | $\eta_{\text {PH }}$ | Efficiency of PHS | | $N_{\text {rmax }}$ | Maximum repetitions of optimal solution | $\eta_{g} / \eta_{p}$ | Generating/Pumping power efficiency of PHS | | PSR req,t | Spinning reserve requirements at period <br> $t$ | $\tau_{g} / \tau_{p}$ | Number of periods of PHS generating/pumping power | | $\begin{aligned} & \text { PSR } W, t / P S R \\ & \quad P v, t \end{aligned}$ | Spinning reserve requirements to cope with the uncertainty of wind/PV | $\omega 1 / \omega 2$ | Regulating factor, the value can be larger in the early iteration and then gradually reduced | | $\begin{aligned} & \text { Ppeak D, } t / \\ & \text { Pvalley D, } t \end{aligned}$ | Load demand at peak/ valley period | $\delta$ | Deviation threshold | | Ppeak W,t/ <br> Ppeak $P v, t$ <br> Pvalley W, <br> $t / P$ valley <br> $P v, t$ | Available wind/PV at peak/valley load period. | $\lambda$ | Positive factor $(0<\lambda<1$ ), determined by overall deviation and operational ability of PHS | | $\begin{aligned} & \text { PSR,peak req, } \\ & t / P S R, \\ & \text { valley req, } t \end{aligned}$ | Spinning reserve requirements at peak/ valley load | $\Delta \lambda k i$ | Step of the $i_{\text {th }}$ component of the node $k$ | | $P_{i t, j}$ | Output of unit $i$ at period $t$ of the $j_{\text {th }}$ seed | $\Delta t$ | Period interval |

1. Introduction  1. 引言

1.1. Context  1.1. 背景

To cope with the global climate crisis and implement the Paris Agreement, China has proposed the “dual carbon” goal, that is, carbon dioxide emissions strive to peak by 2030 and strive to achieve carbon neutrality by 2060 [1]. To achieve this goal, constructing new power system with high proportion of renewable energy sources (RES) such as wind power and photovoltaic (PV) is a feasible and effective way. However, the access of large-scale stochastic intermittent RES has seriously affected the stability of power source [2]. Thus, the system not only needs to maintain the balance between supply and demand, but also needs sufficient flexible regulation ability to cope with the strong randomness and volatility of RES [3,4]. In the future, China’s power system will be a multi-source complementary system, so it is particularly significant to carry out optimal scheduling of multi-type heterogeneous power source coupled system [5-8]. How to fully motivate the flexibility of different power sources and make best use of multi-energy complementary properties to promote the system comprehensive effectiveness is an urgent problem to be solved.
为应对全球气候危机，落实《巴黎协定》，中国提出了“双碳”目标，即二氧化碳排放力争到 2030 年达到峰值，力争 2060 年前实现碳中和 [1]。为了实现这一目标，构建风电和光伏 （PV） 等可再生能源 （RES） 比例高的新型电力系统是一种可行且有效的方法。然而，大规模随机间歇性 RES 的接入严重影响了电源的稳定性 [2]。因此，系统不仅需要保持供需平衡，还需要足够的灵活调节能力来应对 RES 强大的随机性和波动性 [3,4]。未来，我国电力系统将是多源互补系统，因此对多类型异构电源耦合系统进行优化调度显得尤为重要 [5-8]。如何充分激发不同动力源的灵活性，充分利用多能量互补特性，促进系统综合效能，是一个亟待解决的问题。
In 2023, more than 60 % 60 % 60%60 \% of China’s power generation is borne by thermal power, and it still plays an irreplaceable role in ballast, supply and regulation in power system [9]. RES generation presents seasonal, extreme fluctuations, and unbalanced spatial and temporal distribution, resulting in a small proportion of effective integration into the power system, and more power generation borne by thermal power units (TPUs), which makes China one of the largest greenhouse-gas emitters [10]. Therefore, promoting the efficient consumption of RES, optimizing the energy structure of power generation, and implementing effective carbon emission reduction strategies are currently urgent issues to be addressed [11]. Enhancing the flexible regulation ability of system is one of the important means to promote the efficient utilization of RES. Thermal is widely recognized as the main flexible regulation power source to alleviate the fluctuation of RES [12]. However, relying solely on the regulation capacity of thermal power plants (TPP) will not only lead to frequent start-stop operations and over-limit climbing rates, but also affect the low-carbon economic operation [13]. Then, some scholars have proposed that using general hydropower plants (GHP) with fast and flexible regulation can complement the uncertainty of RES and reduce the dependence on TPP [14]. However, frequent variable load regulation will increase the risk of operation in the vibration zone [15]. Pumped hydro storage (PHS) with fast response capability has attracted great attention from researchers [16,17], and has strong adaptability to RES generation and great combined operation effect, which has become the optimal choice to develop high-efficiency regulated power and energy storage facilities. Therefore, since 2022, China has introduced a series of policies to encourage the development of PHS. According to the National Energy Administration’s “Medium and Long-term Development Plan for PHS”, it is proposed that by 2025 and 2030, the total scale of PHS will reach more than 62 GW and 120 GW respectively [18]. In summary, it is of great significance to establish a multi-source coupling mechanism of wind-PV-hydropower-thermal-pumped hydro storage (WPHTPHS), fully utilize green flexible PHS and GHP with traditional inefficient TPP to coordinated balance the inherent characteristics of RES, to realize the safe, efficient and low-carbon economic operation of system and assists “dual carbon”.
到 2023 年，我国的发电量超过 60 % 60 % 60%60 \% 火力发电量，火力发电在电力系统中的镇流器、供电和调节方面仍然发挥着不可替代的作用 [9]。可再生能源发电具有季节性、极端波动性和不平衡的时空分布，导致有效并入电力系统的比例很小，而更多的发电量由火电机组 （TPU） 承担，这使得中国成为最大的温室气体排放国之一 [10]。因此，促进可再生能源的高效消费、优化发电能源结构、实施有效的碳减排策略是当前亟待解决的问题 [11]。增强系统的柔性调节能力是促进可再生能源高效利用的重要手段之一。热被广泛认为是缓解可再生能源波动的主要柔性调节动力源 [12]。然而，单纯依赖火电厂 （TPP） 的调节能力不仅会导致频繁的启停运行和超限爬升速度，还会影响低碳经济运行[13]。然后，一些学者提出，使用具有快速灵活调节功能的一般水电站 （GHP） 可以补充 RES 的不确定性并减少对 TPP 的依赖 [14]。然而，频繁的可变负载调节会增加在振动区运行的风险 [15]。具有快速响应能力的抽水蓄能（PHS）引起了研究人员的高度关注[16,17]，并且对RES发电具有很强的适应性和良好的联合运行效果，已成为发展高效稳压电力和储能设施的最佳选择。 因此，自 2022 年以来，中国出台了一系列政策鼓励 PHS 的发展。根据国家能源局《小灵通中长期发展规划》，提出到 2025 年和 2030 年，小灵通总规模分别达到 62 GW 和 120 GW 以上 [18]。综上所述，建立风-光-水-热-抽水蓄能（WPHTPHS）多源耦合机制，充分利用绿色柔性PHS和GHP与传统低效TPP，协调平衡可再生能源的固有特性，实现系统安全、高效、低碳的经济运行，助力“双碳”发展具有重要意义。

1.2. Literature review  1.2. 文献综述

In recent years, many studies have focused on the optimal scheduling of multi-energy coupled models and methods. For example, Yuan et al. [19] used Markov chain to generate a large number of random scenarios to predict wind power, a dynamic load economic scheduling model with wind-thermal is established, and the influence of different wind power confidence intervals on system economy is analyzed. In Ref. [20], a hydropower-thermal-wind short-term complementary optimization scheduling model is proposed to minimize power generation cost and carbon emission, the valve point effect and various complex nonlinear constraints are considered, thus presents the characteristics of high dimension, non-convexity and nonlinearity. A heuristic constraint processing technology and violation regulation method are proposed to solve the problem. Wang et al. [21] established a scheduling model of wind-PV-hydropower-thermal multi-source complementary and multi-regional coordinated operation by minimizing fluctuation of thermal power output and maximizing consumption of RES, and adopted the adaptive synchronous peak-shaving strategy of GHP to balance the fluctuation of RES output. Wang et al. [22] proposed a short-term hydropower-PV complementary optimal scheduling model by maximizing the trade-off between power supply reliability and economy, and adopted a multi-constraint method to convert multiple objectives into a single objective to obtain the optimal solution. In Ref. [23], a two-stage robust optimal model of hydropower-PV-thermal hybrid system adapted to PV uncertain scenarios by minimizing water consumption in the day-ahead stage was constructed, and the optimal start-stop scheme of TPUs and the optimal operation area of GHP were determined. The optimization objectives among the above researchers mainly focus on
近年来，许多研究都集中在多能量耦合模型和方法的最优调度上。例如，Yuan et al. [19] 使用马尔可夫链生成大量随机情景来预测风电，建立了具有风热的动态负荷经济调度模型，并分析了不同风电置信区间对系统经济性的影响。在参考文献[20]中，提出了一种水电-火-风短期互补优化调度模型，以最小化发电成本和碳排放，考虑了阀点效应和各种复杂的非线性约束，从而呈现出高维、非凸性和非线性的特点。针对该问题，提出了一种启发式约束处理技术和违规规制方法。Wang等[21]通过最小化火电出力波动和最大化RES消纳，建立了风-光-水-电多源互补、多区域协同运行的调度模型，并采用GHP的自适应同步调峰策略来平衡RES出力的波动。Wang等[22]通过最大化供电可靠性和经济性之间的权衡，提出了一种短期水电-光伏互补的最优调度模型，并采用多约束方法将多个目标转换为单个目标以获得最优解。在参考文献 [23] 中，通过最小化前一天的用水量，构建了适应光伏不确定性情景的两阶段鲁棒性水电-光伏-热混合系统最优模型，并确定了 TPU 的最佳启停方案和 GHP 的最佳运行区域。上述研究人员中的优化目标主要集中在
the minimum economic cost, minimum carbon emission, maximum power supply reliability, maximum clean energy consumption, etc. But most only consider one or several combinations of these optimization objectives, and there are few studies comprehensively consider them. Precisely because of this, whether in theoretical research or practical application, there are defects in the consumption of wind power and PV at the expense of other power sources’ operation efficiency, when the proportion of RES increases to a certain extent, there will inevitably be a phenomenon that the gain is not worth the loss.
最低的经济成本、最低的碳排放、最大的供电可靠性、最大的清洁能源消耗等。但大多数只考虑了这些优化目标的一种或几种组合，很少有研究全面考虑它们。正因为如此，无论是在理论研究还是实际应用中，都存在以牺牲其他电源运行效率为代价的风电和光伏消纳缺陷，当可再生能源的比例达到一定程度时，必然会出现得不偿失的现象。
With the advancement of clean and low-carbon energy transformation, TPUs will also face the demand for flexible transformation [24]. In this context, the multi-source co-scheduling begins to pay attention to the flexibility indicators such as the deep peak shaving capacity and spinning reserve benefit of TPUs, and continuously tap the reserve space to cope with the randomness of RES [25]. For example, Zhu et al. [26] established a two-stage distributed robust optimization day-ahead scheduling model considering deep peak shaving of TPUs in uncertain RES integration, which reduced the pressure of thermal power peak regulation while ensuring the efficient consumption of RES. In Ref. [27], by considering the large change of the TPUs operation cost after deep peak shaving condition, a new mechanism of wind-thermal combined system based on interval optimization is proposed to obtain a better cost interval and significantly improve the permeability of wind power. However, blindly tapping the flexible regulation potential of TPUs will reduce the units’ operation life and bring additional cost. TPUs is limited by the start-stop time, the response speed is slow, and cannot respond to RES’ variation in real time.
随着能源清洁低碳转型的推进，TPU 也将面临柔性转型的需求 [24]。在此背景下，多源协同调度开始关注 TPU 的深度调峰能力和旋转储备效益等灵活性指标，并不断挖掘储备空间以应对 RES 的随机性 [25]。例如，Zhu 等[26]建立了一个两阶段分布式鲁棒优化日前调度模型，考虑了不确定的可再生能源集成中TPU的深度调峰，在保证可再生能源高效消纳的同时，减轻了火电调峰的压力。在参考文献[27]中，通过考虑深度调峰后TPU运行成本的较大变化， 提出了一种基于区间优化的风热联合系统新机制，以获得较优的成本区间，显著提高风电的渗透率。然而，盲目挖掘 TPU 的灵活调节潜力会缩短装置的使用寿命并带来额外的成本。TPU 受启停时间的限制，响应速度慢，无法实时响应 RES 的变化。
Considering the fast start-stop and good tracking ability, flexibly regulated hydropower can suppress the RES fluctuations and mitigate the flexibility deficit caused by deep peaking. Therefore, scholars began to explore the feasibility of complementary operation of hybrid energy sources such as hydropower-PV [28], hydropower-wind [29], hydropower-wind-thermal [30], and hydropower-wind-PV [31]. In Reference [32], the concept of variable reserve capacity was introduced into the hydropower-PV complementary model, and reduced the impact of PV output deviation on the performance of GHP by adjusting the system reserve demand. Hirth [33] studied the impact of hydropower compensation for wind power on market value. In Ref. [34], the decision management of peak-shaving, valley-filling and generation in the integrated operation of wind-hydropower-thermal, the maximum utilization of wind power and the substitution of hydropower units for TPUs are realized. Lin et al. [35] adopted the chance constrain model to predict the error distribution of wind and PV, and the hydropower coordination system peaking operation to avoid power shortages. These studies highlight the advantages of hydropower flexibility in multi-source coupled systems, but ignore operation characteristics of units, not adequately stimulating the flexibility of hydropower, and even sacrifices the peak regulation benefit.
考虑到快速启停和良好的跟踪能力，灵活调节的水电可以抑制 RES 波动，缓解深度调峰造成的灵活性不足。因此，学者们开始探索水电-光伏 [28]、水电-风能 [29]、水电-风-热 [30] 和水电-风-光伏 [31] 等混合能源互补运行的可行性。在参考文献 [32] 中，将可变储量的概念引入水电-光伏互补模型，通过调整系统储量需求来减少光伏出力偏差对 GHP 性能的影响。Hirth [33] 研究了风电水电补偿对市场价值的影响。参考文献[34]实现了风-水-热一体化运行中调峰、填谷、发电的决策管理，实现了风电的最大利用和TPU对水电机组的替代。Lin等[35]采用机会约束模型预测风电和光伏的误差分布，并采用水电协调系统调峰操作来避免电力短缺。这些研究强调了水电灵活性在多源耦合系统中的优势，但忽视了机组的运行特性，没有充分激发水电的灵活性，甚至牺牲了调峰效益。
In response to the increasing demand for RES flexibility, the configuration of a certain capacity of PHS or other energy storage facilities is an attractive option. Lu et al. [36] proposed a short-term optimal scheduling strategy for cascade hydropower station with PHS and TPP to consume RES. In Ref. [37], established a two-stage scheduling model with optimal overall efficiency, the load distribution by hydropower in the day-ahead stage, the load deviation smoothed by PHS in the real-time stage, and reliable power generation plan is formulated to suppress the fluctuation of wind power. In Ref. [38] quantitatively evaluated the integration wind power and the reduction system cost by PHS. These studies analyzed how to use PHS to optimize the regulation performance after RES integrated, but the influence of PHS with different installed capacity on coordinated operation is not considered from the regional resource allocation perspective.
为了满足对 RES 灵活性日益增长的需求，配置一定容量的 PHS 或其他储能设施是一个有吸引力的选择。Lu et al. [36] 提出了一种采用 PHS 和 TPP 的梯级水电站消耗 RES 的短期最优调度策略。在参考文献 [37] 中，建立了具有最优整体效率的两阶段调度模型，前一天水电的负荷分配，实时阶段由 PHS 平滑的负荷偏差，并制定了可靠的发电计划来抑制风电的波动。在参考文献 [38] 中，定量评估了 PHS 的并网风电和降低系统成本。这些研究分析了 RES 集成后如何使用 PHS 优化调节性能，但未从区域资源配置角度考虑不同装机容量的 PHS 对协同运行的影响。
Based on the review of existing research, the following limitations were identified.
根据对现有研究的回顾，确定了以下局限性。
(1) RES consumption will occupy the power space of conventional power sources, resulting in inefficient operation of some units and aggravating the conflict of interest among the system.
（1） RES 消纳会占用常规电源的电力空间，导致部分机组运行效率低下，加剧系统内部的利益冲突。
(2) Heuristic algorithms are suitable for solving complex optimization problems in multi-source coupled systems, but they struggle to guarantee global optimality in high-dimensional stochastic variable solution spaces.
（2） 启发式算法适用于解决多源耦合系统中的复杂优化问题，但它们难以保证高维随机变量解空间中的全局最优性。

1.3. Contributions  1.3. 贡献

To overcome these limitations, this paper adapts to the scheduling requirements of new power system with large-scale RES, and takes the large-scale regional power grid with five types of heterogeneous power sources including wind, PV, GHP, PHS and TPP as the research object. A scheduling method that can fully motivate the role of each power source, promote complementary advantages, and make up for shortcomings is designed, and a hierarchical sequence optimization strategy with PHS priority regulation, hydropower follows and thermal power last regulation is proposed from multiple perspectives such as economic cost, environmental benefit, clean energy consumption and operating characteristics, to obtain the optimal scheduling scheme. The main contributions are as follows.
为了克服这些限制，本文适应了大规模可再生能源新型电力系统的调度要求，以风电、光伏、GHP、PHS和TPP等五类异构电源的大规模区域电网为研究对象。设计了一种能够充分发挥各电源作用、促进优势互补、补短板的调度方法，从经济成本、环境效益、清洁能源消纳、运行特性等多个角度，提出了PHS优先调控、水电跟控、火电后调的分层序列优化策略。 获取最优调度方案。主要贡献如下。
(1) A scheduling model of WPHTPHS with four objectives is established to overcome the defect that the RES utilization is at the expense of other power sources’ operation efficiency. The model fully utilizes the complementary characteristics of various power sources, promotes the efficient integration of RES, and ensures low-carbon economy and stable operation of TPUs.
（1） 建立了具有四个目标的 WPHTPHS 调度模型，以克服 RES 利用率以牺牲其他电源运行效率为代价的缺陷。该模型充分利用了各种电源的互补特性，促进了 RES 的高效集成，保证了 TPU 的低碳经济和稳定运行。
(2) Based on the load fluctuation characteristics and system reserve demand, a method for pre-assigning state variables of PHS and TPUs is designed to achieve independent optimization of discrete integer mixed variables, which effectively avoids the dimension disaster problem.
（2）基于负载波动特性和系统储备需求，设计了一种预分配PHS和TPUs状态变量的方法，实现了离散整数混合变量的独立优化，有效避免了维度灾难问题。
(3) A novel multi-objective hierarchical sequence solution method based on priority stratification-coupling feedback idea is proposed to overcome the lack of priority in traditional multiobjective optimization, and an enhanced plant growth simulation algorithm with variable step dual-mode node growth strategy is developed for hierarchical solution. This provides a new idea for the efficient solution of multi-objective scheduling model.
（3）克服传统多目标优化中缺乏优先级的问题，提出了一种基于优先级分层耦合反馈思想的新型多目标分层序列求解方法，并针对分层求解开发了一种具有变步长双模态节点生长策略的增强植物生长模拟算法。这为多目标调度模型的高效求解提供了新思路。
(4) The proposed model and solution method can maximize the synergistic optimization and mutual benefit of each power source, effectively utilize the flexible regulation capabilities of hydropower and PHS to respond to fluctuations in wind and PV, and coal-fired cost and carbon emission cost of TPUs are greatly reduced.
（4）所提出的模型和求解方法可以最大限度地发挥各电源的协同优化和互利，有效利用水电和PHS的灵活调节能力来应对风电和光伏的波动，大大降低TPUs的燃煤成本和碳排放成本。
The rest of this paper is organized as follows: Section 2 establishes a multi-source coupling model of WPHTPHS considering multi-objective optimization. Section 3 gives the method of solving the state variables of PHS and TPUs. Section 4 proposes a novel model solving strategy. Section 5 discusses and analyzes the operating results. Section 6 summarizes the main conclusions and future work.
本文的其余部分组织如下：第 2 节建立了一个考虑多目标优化的 WPHTPHS 多源耦合模型。第 3 节给出了求解 PHS 和 TPU 状态变量的方法。第 4 节提出了一种新的模型求解策略。第 5 节讨论并分析了经营结果。第 6 节总结了主要结论和未来工作。

2. Multi-source coupled scheduling model of WPHTPHS
2. WPHTPHS 多源耦合调度模型

2.1. Objective function  2.1. 目标函数

The optimal scheduling model of WPHTPHS combined system plays its role by fully utilizing the multi-source complementary characteristics and motivating each power source to enhance the utilization of clean energy while ensuring the economic and stable operation of the system. Therefore, multiple optimization objectives comprehensively consider the operation cost and stability of TPUs, the utilization of clean energy
WPHTPHS 组合系统的最优调度模型通过充分利用多源互补特性并激励每个电源提高清洁能源的利用率，同时保证系统的经济稳定运行，从而发挥作用。因此，多个优化目标综合考虑了 TPU 的运营成本和稳定性、清洁能源的利用
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